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In this work, we propose an approach for computing the positive solution of a fully fuzzy linear system where the coefficient matrix is a fuzzy n×n matrix. To do this, we use arithmetic operations on fuzzy numbers that introduced by Kaffman in [18] and convert the fully fuzzy linear system into two n × n and 2n × 2n crisp linear systems. If the solutions of these linear systems don't satisfy in positive fuzzy solution condition, we introduce the constrained least squares problem to obtain optimal fuzzy vector solution by applying the ranking function in given fully fuzzy linear system. Using our proposed method, the fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

This paper presents a new approach to compare fuzzy numbers using α-distance. Initially, the metric distance on the interval numbers based on the convex hull of the endpoints is proposed and it is extended to fuzzy numbers. All the properties of the α-distance are proved in details. Finally, the ranking of fuzzy numbers by the α-distance is discussed. In addition, the proposed method is compared with some known ones, the validity of the new method is illustrated by applying its to several group of fuzzy numbers.

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